Aggregating Judgements: Logical and Probabilistic Approaches

Instructor: Eric Pacuit (website)

ESSLLI 2018 • Sofia University St. Kl. Ohridski, Sofia, Bulgaria

August 5 - 10, 2018

17:00 - 18:30 • Room 255, Floor 2

This course will introduce the key results (including proofs) and the main research themes in the study of judgement aggregation and the wisdom of the crowds. The course will focus on both logical and probabilistic models of judgement aggregation. The primary objective is to introduce the main mathematical methods and conceptual ideas found in this literature. In addition, I will state and prove the central results found in this literature. To facilitate understanding the main proof techniques and results, I will spend much of the time working through the theorems at the blackboard.

Of course, there is a large literature concerning each of the theorems and topics listed above. My goal will not to be to survey this entire literature. Instead, I present enough background material to state and prove each of the theorems mentioned above. This will provide students with a solid foundation to engage with this fascinating research area.

Day 1: Introduction to judgement aggregation

August 6, 2018

C. List, Social Choice Theory, Stanford Encyclopedia of Philosophy, 2013

E. Pacuit, Condorcet Jury Theorem: Jupyter notebook

Day 2: Impossibility theorems and characterization results

August 7, 2018

U. Endriss, Judgment Aggregation. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, editors, Handbook of Computational Social Choice, Cambridge University Press, 2016. (For a somewhat different perspective than what I presented during the lecture)

Day 3: Probabilistic opinion pooling

August 8, 2018

F. Dietrich and C. List, Probabilistic opinion pooling, Oxford Handbook of Probability and Philosophy, 2016

Day 4: Distance-based aggregation; opinion dynamics; Aumann's agreeing to disagree theorem

August 9, 2018

Day 5: Opinion merge; belief polarization; concluding remarks

August 10, 2018